Characteristic curve for asynchronous drives
Asynchronous motors are often used for spindle drives. You can achieve optimised adaptation to typical characteristic of such spindle drives using the speed-dependent spindle acceleration curve a=f(n) shown in the figure below.
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In addition to maximal permissible acceleration a_max and speed N1 in constant range of acceleration curvature only setting to the speed N2 has to be done. Above speed value N1 the acceleration curve has a proportional characteristic to 1/n, above speed value N2 it is proportional to 1/n².